area under the curve

Hi I would like to know where I went wrong. QN: A region with x more than and equal to 0 has boundaries defined by y=sinx , y=cosx and the y-axis. Find the area of that region. Since we are integrating along the y-axis, I made x the subject so in the end my integral for the area was integrating from y= 0 to y= 1 of arccosy-arcsiny with respect to y. Using integration by parts abd all, my final answer was 2-pi/2. Where did I go wrong! Thank you so much for your help!

Re: area under the curve

Since you don't show details of your calculation, it isn't possible to say where you went wrong.
However, why complicate matters ? You can integrate wrt to x as usual. Just find the area under the cosine curve and subtract the area under the sine curve. The limits for x will be x=0 and the x coordinate of the point of intersection of the two curves.